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Explicit reduction modulo p of certain crystalline representations

PU/IAS Number Theory

Explicit reduction modulo p of certain crystalline representations

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Toby Gee, Imperial College and Northwestern University

We use the $p$-adic local Langlands correspondence for $GL_2(Q_p)$ to explicitly compute the reduction modulo $p$ of crystalline representations of small slope, and give applications to modular forms.Joint work with Kevin Buzzard.